The two Manchester clubs will meet in the FA Cup final at Wembley on June 3.
The Red Devils defeated Brighton and Hove Albion on penalties on Sunday while Pep Guardiola's side dispatched Sheffield United 3-0 a day prior to make the showpiece.
Manchester United have already won the Carabao Cup this season after beating Newcastle United 2-0 in February.
City are firmly in the mix for the Premier League title and also have a semi-final date with Real Madrid in the UEFA Champions League.
Only Manchester United in the 1998/1999 season have won the Premier League, FA Cup and Champions League in the same campaign; a feat they will be desperate to prevent their city rivals from emulating.
"I understand, of course, the feelings from the Manchester United fans about it," the Dutchman said.
"We will do everything to give them that, to give them the second trophy, everything that I have, everything the team have, everything the staff have, we will give everything to get that done.
"We can do it, because we proved it, but it's not an easy job. It's a great team, but we'll also have a great team and great players and we can beat them.
"More than 100 per cent, you can't do, so the fans can rely on that. We will give it and we will do it against every opponent, it doesn't matter who it is.
"Of course, we want to give that against City. We want to give the fans that, sure."
